President Abdrabbuh Mansour Hadi was reported to be inside the house but an official insisted he was safe.

The UN Security Council condemned the attack and urged the rebels to respect the country's legitimate leaders.

But rebel leader Abdel Malek al-Houthi accused Yemen's leaders of corruption and said the country was at a "defining" moment.

The attack on Mr Hadi's home came after the rebels entered the presidential palace in another part of the city following a brief clash with guards.

Yemen, a key US ally in the fight against al-Qaeda in the region, has been beset by unrest for months.

Houthi militias, who are seeking greater autonomy for their home province, overran Sanaa in September after moving out of their northern stronghold.

However, the capital's presidential buildings have so far remained outside their control.

President 'fine'

Information Minister Nadia al-Sakkaf said on Twitter the president's home had come under heavy shelling from armed forces positioned on rooftops nearby.

An unnamed Yemeni government official told Reuters news agency: "The president is inside and he is fine." Another official said two people had been killed in the fighting.

Shelling died down after about half an hour, witnesses said.

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The rebels have set up checkpoints in Sanaa

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The rebel leader's speech was broadcast live

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President Hadi has been under pressure for months

In a live televised address, the rebel leader accused President Hadi and others of putting their interests ahead of the people's.

"What happened was that they [the political leadership] sank deep into corruption and tyranny," he said.

"The nation has started moving towards a tragic situation and complete collapse. The situation has worsened on all fronts - political, economic and security - on a large scale."

Mr Houthi said the government had encouraged the spread of al-Qaeda.

The ceasefire that broke down on Tuesday had been agreed just one day earlier after hours of fierce clashes in the city between the presidential guard and the rebels.

Under an agreement with President Hadi, the Houthis - who abducted presidential chief of staff Ahmed Awad Bin Mubarak on Saturday - pledged to withdraw from the capital once a new unity government was formed.

UN appeal

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Houthi rebels in Sanaa on Tuesday

In a statement adopted by all 15 members, the UN Security Council said President Hadi was "the legitimate authority".

It urged "all parties and political actors in Yemen" to stand with him and the government to "keep the country on track to stability and security".

The UN special envoy to Yemen, Jamal Benomar, had told members via video link that the Houthis had persuaded other military units not to fight them, a diplomat at the closed-door session told Reuters.

The Houthis, who adhere to a branch of Shia Islam known as Zaidism, have staged periodic uprisings since 2004 in an effort to win greater autonomy for their northern heartland of Saada province.

They consolidated their control over Saada during the 2011 uprising that forced long-time President Ali Abdullah Saleh to step down.

Since July the rebels have inflicted defeats on tribal and militia groups backed by the leading Sunni Islamist party, Islah, and battled jihadist militants from al-Qaeda in the Arabian Peninsula (AQAP), which has vowed to defend the country's Sunni community.

Opponents allege that the rebels ultimately hope to reinstall the Zaidi imamate, which ruled North Yemen for almost 1,000 years until 1962.